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Full text of "Treatise On Analysis Vol-Ii"

viii        CONTENTS

group. 6. Examples and particular cases of convolution of measures.
7. Algebraic properties of convolution. 8. Convolution of a measure and a func-
tion. 9. Examples of convolutions of measures and functions. 10. Convolution
of two functions. 11. Regularization.

Chapter XV


1. Normed algebras. 2. Spectrum of an element of a normed algebra. 3. Charac-
ters and spectrum of a commutative Banach algebra. The Gelfand transformation.
4. Banach algebras with involution. Star algebras. 5. Representations of algebras
with involution. 6. Positive linear forms, positive Hilbert forms, and representa-
tions. 7. Traces, bitraces, and Hilbert algebras. 8. Complete Hilbert algebras.
9. The Plancherel-Godement theorem. 10, Representations of algebras of con-
tinuous functions. 11. The spectral theory of Hilbert. 12. Unbounded normal
operators. 13. Extensions of hermitian operators.

References...................   . m......444

Index.............................447                                    set of elements xy with x e A and y e B,